24x^2-160=0

Solution for 24x^2-160=0 equation:

24x^2-160=0

a = 24; b = 0; c = -160;
Δ = b2-4ac
Δ = 02-4·24·(-160)
Δ = 15360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15360}=\sqrt{1024*15}=\sqrt{1024}*\sqrt{15}=32\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{15}}{2*24}=\frac{0-32\sqrt{15}}{48}
=-\frac{32\sqrt{15}}{48}
=-\frac{2\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{15}}{2*24}=\frac{0+32\sqrt{15}}{48}
=\frac{32\sqrt{15}}{48}
=\frac{2\sqrt{15}}{3}
$